李雅普诺夫运动稳定性理论在大跨度拱型结构中的应用  

Application of stability theory of Lyapunov motion to large-span arch structures

作　　者：吴东平[1] 

机构地区：[1]武汉科技大学城市建设学院,湖北武汉430060

出　　处：《武汉大学学报（工学版）》2012年第5期627-629,647,共4页Engineering Journal of Wuhan University

基　　金：湖北省自然科学基金项目(编号:2006ABA291)

摘　　要：基于Lyapunov运动稳定性理论,经过推导可知,一个单自由度的某一个受迫振动的特解的运动稳定性问题等价于这个单自由度系统自由振动的稳定问题.对于复杂非线性系统的动力稳定性问题,直接应用Lyapunov理论进行系统的动力稳定性判定比较困难,考虑大跨度拱型结构的变形特征,提出一种简洁、实用且适合数值计算的动力稳定性判别方法——位移时程变化法.运用该方法计算结构在承受一般动荷载类型和不同计算条件下的动力稳定性,验证此方法的实用性及正确性.Based on the stability theory of Lyapunov motion,it can be derived that the motion stability problem of a particular solution to a forced vibration of a single degree of freedom system,is equal to the stability problem of the free vibration system of single degree of freedom.For a dynamic stability problem of complex nonlinear system,it is difficult to judge the dynamic stability of a system by the theory of Lyapunov motion directly.Considering the deformation feature of a large-span arch structure,a simple and practical theory named deformation history theory which is suitable for digital computation to judge the dynamic stability of an arch structure is put forward and used to judge the dynamic stability of an arch structure under common dynamic loading and different conditions.It is shown that the theory is applicable and reasonable.

关 键 词：运动稳定性 动力失稳 数值计算 有限元 

分 类 号：TU393.3[建筑科学—结构工程]